Beyond birthday secure domain preserving PRFs from a single permutation

This paper revisits the fundamental cryptographic problem of building pseudorandom functions (PRFs) from pseudorandom permutations (PRPs).We prove that, SUMPIP, i.e. P⊕P^{−1}, the sum of a PRP and its inverse, and EDMDSP, the single-permutation variant of the “dual” of the Encrypted Davies–Meyer sch